Effect of random secondary delay times and emission velocities in electron multipactors

Traditionally, the modeling of rf driven electron cascades (multipactors) has employed a constant emission velocity and zero delay time for all secondaries. This paper introduces the effects from the random secondary emission velocities, as well as the random delay time in the secondary emission, By combining the emission related random phase kicks with the focusing rf action it is shown that the electron impact phase, though wandering erratically, nevertheless stays in the vicinity of a stable phase-locked multipactor phase; the rms phase deviation from phase locking is bounded and directly proportional to the rms fluctuation in the secondary emission. The random phase wandering around the locked phase reduces the nominal secondary emission coefficient delta to an effective value delta* between delta > delta* greater than or equal to delta/2 and depending not only on the impact energy of the primary but also on the thermal spread of the secondaries. Multipactor quenching from secondary spreads may occur through the reduction in delta*. For sufficiently small fluctuations, the modeling of a ''cold'' multipactor with zero thermal spreads is sufficient to determine the actual multipactor behavior in terms of only two control parameters; the normalized rf and magnetic field strengths.